First consider the expression for: Take the product of $-4$ and $x$ and add $7$. Now select the answer that matches the following: The sum of $-5$ and the product of $7$ and that expression.
Solution: Let's break this problem into smaller and easier pieces. What is the product of $-4$ and $x$ $-4 \times x = \color{orange}{-4x}$ What does adding $7$ to $-4x$ do? $-4x$ $ + 7$ What is the quantity of $7$ times that expression $7 \times (-4x + 7) = \color{orange}{7(-4x+7)}$ What is the sum of $-5$ and $\color{orange}{7(-4x+7)}$ $7(-4x+7)$ $ - 5$ So the entire expression we're considering can be written as $7(-4x+7)-5$.